Turner et al. (1992) uses logistic regression to estimate the rate at which picloram, a herbicide, kills tall larkspur, a weed. Their data was collected by applying four different levels of picloram to separate plots, and the number of weeds killed out of the number of weeds within the plot was recorded. The data are in the file picloram.csv.29 Complete the following:
(a) Estimate a logistic regression model using the picloram amount as the explanatory variable and the number of weeds killed as the response variable.
(b) Plot the observed proportion of killed weeds and the estimated model. Describe how well the model fits the data.
(c) Estimate the 0.9 kill rate level ("LD90") for picloram. Add lines to the plot in (b) to illustrate how it is found (the segments() function can be useful for this purpose).
(d) To calculate a confidence interval for the dosage that yields a 0.9 kill rate, below is a set of R code:
that uses Equation 2.21 in its calculation. Describe what each line of the R code does and run it to find a 95% confidence interval for x0.g.
(e) What amount of picloram should be used in order to have a 0.9 kill rate?
(f) The data for this problem consist of only four different dosage levels of picloram. What assumptions are needed in order for the model to provide a good estimate of xπ?
